Apprenticeship learning with prior beliefs using inverse optimization

2025-05-27

AI Summary

This paper addresses the ill-posedness of inverse reinforcement learning (IRL) under suboptimal expert demonstrations. We propose a unified, regularized min-max framework that jointly models inverse optimization (IO), IRL, and apprenticeship learning (AL). The framework explicitly incorporates structural prior beliefs about the cost function into the objective via convex–concave minimax formulation and tailored regularization, thereby mitigating solution non-uniqueness. We theoretically establish the convergence of stochastic mirror descent (SMD) under this framework and show that classical apprenticeship learning emerges as its unregularized special case. Empirical results demonstrate that the proposed regularization significantly enhances robustness in cost vector estimation and improves generalization performance of apprentice policies. To our knowledge, this work is the first to achieve structured modeling and analysis of IO, IRL, and AL within a unified probabilistic–optimization perspective.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

The relationship between inverse reinforcement learning (IRL) and inverse optimization (IO) for Markov decision processes (MDPs) has been relatively underexplored in the literature, despite addressing the same problem. In this work, we revisit the relationship between the IO framework for MDPs, IRL, and apprenticeship learning (AL). We incorporate prior beliefs on the structure of the cost function into the IRL and AL problems, and demonstrate that the convex-analytic view of the AL formalism (Kamoutsi et al., 2021) emerges as a relaxation of our framework. Notably, the AL formalism is a special case in our framework when the regularization term is absent. Focusing on the suboptimal expert setting, we formulate the AL problem as a regularized min-max problem. The regularizer plays a key role in addressing the ill-posedness of IRL by guiding the search for plausible cost functions. To solve the resulting regularized-convex-concave-min-max problem, we use stochastic mirror descent (SMD) and establish convergence bounds for the proposed method. Numerical experiments highlight the critical role of regularization in learning cost vectors and apprentice policies.

Problem

• Exploring the relationship between inverse reinforcement learning and inverse optimization for MDPs
• Incorporating prior beliefs on cost function structure into IRL and apprenticeship learning
• Addressing ill-posedness of IRL through regularization in apprenticeship learning

Innovation

• Incorporates prior beliefs into IRL and AL
• Formulates AL as regularized min-max problem
• Uses stochastic mirror descent for convergence